What DB and Why?

Mysql - is just most popular of them all.. (MariaDB is perhaps its future).
PostgreSQL get a plus from me here - great behaviour in a few projects I have made.
NoSQL - is good alternative when you don't like relation type SQL's.

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Whichever one you're most comfortable with.

Seriously, though, while the fanboys may say MySQL is over, it's not. MySQL is still the king of the web. Percona is a drop-in replacement for it that can run faster and use less resources.

Postress has some very unique features and is a very good option. Also fairly decently supported in hosts.

NoSQL works fantastically for some things. The performance hype that I've seen though, didn't hold up in my experiences with it, if you needed to have 100% reliable data integrity it came in close to MySQL speed. It does require a slightly different way of thinking about your data, though, and I found it to be easier in some ways, and more difficult in others.

Really boils down to your app's needs, and hosting requirements, and what you and your team already knows, or how much time they have to learn something new.

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I use Firebird SQL. Small footprint. No limits on database size.

http://www.firebirdsql.org/

Lot of good drivers available.

Heavy relational data, full text searching: My/MSSQL
Frequent read, infrequent writes: noSQL (CouchDB)

PouchDB is going to change the face of web development forever. Offline apps cannot be done any other way and since My/MSSQL offer no form of native conflict resolution I don't see this changing in the near future.

Really what it comes down to is your data requirements. If you have a lot of relationships, need painless full text searching, or frequently write changes My/MSSQL are always going to be favoured. If you have frequent reads and infrequent writes (Twitter, FB, etc) Node/noSQL will destroy traditional systems in terms of performance by a very wide margin.

Node/IO.js uses OS threads to manage requests all of which are non-blocking. You can easily handle ten's of thousands of concurrent requests on a simple box as each request uses KB of RAM. Compare that with Apache/IIS which allocate several MB per request and you'll quickly see why a lot of dev's are using it for certain types of apps.

During the last World Cup Twitter set a new record of 618,725 tweets per minute. I'd love to see Apache + My/MSSQL handle that!

Learn both. Each has their use case and frameworks like Ember/Angular are here to stay.